1. Field of the Invention
The present invention relates to a method and apparatus for interferometrically measuring wavefronts commonly encountered in optical metrology. More particularly, the invention relates to apparatus for use in conjunction with either plano or spherical unequal path interferometers for the purpose of rapidly and accurately measuring the distortion of either surfaces or transmitted wavefronts. No physical contact with the article under test is required.
2. The Prior Art
The use of interferometry to measure optical components and systems has grown significantly due to technological advances in lasers, photosensors, and microcomputers. At the same time relatively low-cost instruments have become more widely available for automatic data analysis and quantitative evaluation of interference patterns; see, for example, C. Zanoni, "Interferometry," The Optical Industry and Systems Purchasing Directory, Book 2, pp. E-80-E-82 (1983).
Two different approaches are used to perform wavefront measurements. In the first approach, fringe pattern interferometry (FPI), the optical path difference between the two wavefronts of the interferometer is calculated from the positions of the fringe centers in either a photographed or a real time interference pattern; see, for example, R. A. Jones and P. L. Kadakia, "An Automated Interferogram Technique," Applied Optics, vol. 7, pp. 1477-1482 (1968); Zanoni, U.S. Pat. No. 4,159,522 issued June 26, 1979, and Zanoni, U.S. Pat. No. 4,169,980 issued Oct. 2, 1979.
In the second approach, phase measuring interferometry (PMI), the optical path difference between the two wavefronts of the interferometer is measured at each resolution element of the detector while phase modulating the interference pattern; see, for example, J. H. Bruning, et al., "Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses," Applied Optics, vol. 13, pp. 2693-2703 (1974); Gallagher, et al., U.S. Pat. No. 3,694,088 issued Sept. 26, 1972; N. Balasubramanian, U.S. Pat. No. 4,225,240 issued Sept. 30, 1980; M. Schaham, Proceedings SPIE, vol. 306, pp. 183-191 (1981); and H. Z. Hu, "Polarization heterodyne interferometry using a simple rotating analyzer. 1: Theory and error analysis," Applied Optics, vol., 22, pp. 2052-2056 (1983).
Fringe pattern interferometry, however, is sensitive to geometrical distortions and provides low data density (direct sampling is only on the fringe centers) thereby limiting overall system accuracy. Furthermore, because of the difficulty involved in automatically following complex fringe patterns with FPI, its use is limited to patterns with relatively simple geometry.
Thusly, fringe pattern interferometry provides an adequate technique for wavefront measurements where: (1) the fringe pattern is simple, (2) low-to-modest data density is adequate; (3) the test aperture is very large (i.e., other than simply concave); and (4) the fringe pattern is recorded photographically.
Phase measuring interferometry is capable of providing high data density and is insensitive not only to the intensity profile of the beam but also to the geometrical distortion in the optics or detector to first order. This makes phase measuring interferometry potentially more accurate than fringe pattern interferometry. It also enables the measurement of wavefronts of any fringe geometry and complexity as longe as the maximum fringe density does not exceed one fringe/two resolution elements (pixels) of the detector.
In prior art phase measuring techniques, the optical path difference, or phase, between the two wavefronts of the interferometer is altered, or modulated, by a known amount by one of the following means: (1) mechanically moving an optical element of the interferometer with a piezoelectric transducer, (2) rotating a phase retardation plate in the interferometer, (3) use of either an acousto-optic, electro-optic, or similar device in the interferometer, and (4) variation of the incident angle, see for example, Moore, U.S. Pat. No. 4,325,637 issued Apr. 20, 1982. Most of the prior-art phase modulators require the use of refractive optics in the measurement leg of the interferometer for either large aperture or fast spherical measurements. The refractive optics are not only a serious source of error but also quite expensive. The mechanical motion of an optical element of the interferometer cavity in the prior-art methods must be an extremely precise, tilt-free translation in a straight line. Furthermore, when an optical element with a non-plano surface must be moved to achieve the phase modulation, elaborate corrections must be made in the data analysis, see for example R. C. Moore, "Direct measurement of phase in a spherical-wave Fizeau interferometer," Applied Optics, vol. 19, pp. 2196-2200 (1980). Variation of the incident angle is useful for low precision, plano measurements. Specifically, all of the prior art modulation techniques are expensive and introduce significant measurement errors when large aperture plano or fast spherical wavefront measurements are required.
While prior-art modulation techniques are useful for some applications, it is desirable to do phase measuring interferometry with a modulation technique which is not subject to the problems inherent in the prior-art modulation techniques.